***************************************************************************** * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2019 The FindStatCrew * * * * This information is distributed in the hope that it will be useful, * * but WITHOUT ANY WARRANTY; without even the implied warranty of * * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. * ***************************************************************************** ----------------------------------------------------------------------------- Statistic identifier: St001946 ----------------------------------------------------------------------------- Collection: Parking functions ----------------------------------------------------------------------------- Description: The number of descents in a parking function. This is the number of indices $i$ such that $p_i > p_{i+1}$. ----------------------------------------------------------------------------- References: [1] Schumacher, P.R.F. Descents in Parking Functions, Journal of Integer Sequences, Vol. 21 (2018), Article 18.2.3. [[https://www.emis.de/journals/JIS/VOL21/Schumacher/schu5.pdf]] ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: [1] => 0 [1,1] => 0 [1,2] => 0 [2,1] => 1 [1,1,1] => 0 [1,1,2] => 0 [1,2,1] => 1 [2,1,1] => 1 [1,1,3] => 0 [1,3,1] => 1 [3,1,1] => 1 [1,2,2] => 0 [2,1,2] => 1 [2,2,1] => 1 [1,2,3] => 0 [1,3,2] => 1 [2,1,3] => 1 [2,3,1] => 1 [3,1,2] => 1 [3,2,1] => 2 [1,1,1,1] => 0 [1,1,1,2] => 0 [1,1,2,1] => 1 [1,2,1,1] => 1 [2,1,1,1] => 1 [1,1,1,3] => 0 [1,1,3,1] => 1 [1,3,1,1] => 1 [3,1,1,1] => 1 [1,1,1,4] => 0 [1,1,4,1] => 1 [1,4,1,1] => 1 [4,1,1,1] => 1 [1,1,2,2] => 0 [1,2,1,2] => 1 [1,2,2,1] => 1 [2,1,1,2] => 1 [2,1,2,1] => 2 [2,2,1,1] => 1 [1,1,2,3] => 0 [1,1,3,2] => 1 [1,2,1,3] => 1 [1,2,3,1] => 1 [1,3,1,2] => 1 [1,3,2,1] => 2 [2,1,1,3] => 1 [2,1,3,1] => 2 [2,3,1,1] => 1 [3,1,1,2] => 1 [3,1,2,1] => 2 [3,2,1,1] => 2 [1,1,2,4] => 0 [1,1,4,2] => 1 [1,2,1,4] => 1 [1,2,4,1] => 1 [1,4,1,2] => 1 [1,4,2,1] => 2 [2,1,1,4] => 1 [2,1,4,1] => 2 [2,4,1,1] => 1 [4,1,1,2] => 1 [4,1,2,1] => 2 [4,2,1,1] => 2 [1,1,3,3] => 0 [1,3,1,3] => 1 [1,3,3,1] => 1 [3,1,1,3] => 1 [3,1,3,1] => 2 [3,3,1,1] => 1 [1,1,3,4] => 0 [1,1,4,3] => 1 [1,3,1,4] => 1 [1,3,4,1] => 1 [1,4,1,3] => 1 [1,4,3,1] => 2 [3,1,1,4] => 1 [3,1,4,1] => 2 [3,4,1,1] => 1 [4,1,1,3] => 1 [4,1,3,1] => 2 [4,3,1,1] => 2 [1,2,2,2] => 0 [2,1,2,2] => 1 [2,2,1,2] => 1 [2,2,2,1] => 1 [1,2,2,3] => 0 [1,2,3,2] => 1 [1,3,2,2] => 1 [2,1,2,3] => 1 [2,1,3,2] => 2 [2,2,1,3] => 1 [2,2,3,1] => 1 [2,3,1,2] => 1 [2,3,2,1] => 2 [3,1,2,2] => 1 [3,2,1,2] => 2 [3,2,2,1] => 2 [1,2,2,4] => 0 [1,2,4,2] => 1 [1,4,2,2] => 1 [2,1,2,4] => 1 [2,1,4,2] => 2 [2,2,1,4] => 1 [2,2,4,1] => 1 [2,4,1,2] => 1 [2,4,2,1] => 2 [4,1,2,2] => 1 [4,2,1,2] => 2 [4,2,2,1] => 2 [1,2,3,3] => 0 [1,3,2,3] => 1 [1,3,3,2] => 1 [2,1,3,3] => 1 [2,3,1,3] => 1 [2,3,3,1] => 1 [3,1,2,3] => 1 [3,1,3,2] => 2 [3,2,1,3] => 2 [3,2,3,1] => 2 [3,3,1,2] => 1 [3,3,2,1] => 2 [1,2,3,4] => 0 [1,2,4,3] => 1 [1,3,2,4] => 1 [1,3,4,2] => 1 [1,4,2,3] => 1 [1,4,3,2] => 2 [2,1,3,4] => 1 [2,1,4,3] => 2 [2,3,1,4] => 1 [2,3,4,1] => 1 [2,4,1,3] => 1 [2,4,3,1] => 2 [3,1,2,4] => 1 [3,1,4,2] => 2 [3,2,1,4] => 2 [3,2,4,1] => 2 [3,4,1,2] => 1 [3,4,2,1] => 2 [4,1,2,3] => 1 [4,1,3,2] => 2 [4,2,1,3] => 2 [4,2,3,1] => 2 [4,3,1,2] => 2 [4,3,2,1] => 3 ----------------------------------------------------------------------------- Created: May 24, 2024 at 20:37 by Jennifer Elder ----------------------------------------------------------------------------- Last Updated: May 24, 2024 at 20:37 by Jennifer Elder